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arXiv · 2601.17840

Shifted symplectic structures and Poisson vertex algebra

Wenda Fang
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Abstract

We construct Poisson vertex algebra (PVA) structures on arc spaces from $1$-shifted symplectic (QP) data. A Hamiltonian satisfying the classical master equation induces a canonical PVA $\lambda$-bracket, matching the Hamiltonian-operator formalism for integrable hierarchies. As applications, we find the resulting PVA sheaves on $\mathbb P^1$ and reinterpret our classical $R$-matrix as Maurer-Cartan data in a deformation-theoretic geometric framework, yielding AKS-type integrable hierarchies from the corresponding $R$-deformations.

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Wenda Fang. 2026-01-25. Shifted symplectic structures and Poisson vertex algebra. https://arxiv.org/abs/2601.17840

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